Adaptive SISO algorithms for iterative detection with parametric uncertainty

The soft-input soft-output (SISO) module is the basic building block of any iterative receiver for a system consisting of a network of finite state machines (FSM). It is a trellis based algorithm that provides soft information on the input and output of an FSM, with linear complexity on the decision delay D (or the observation length N). When parametric uncertainty is present, the need for adaptive SISOs arises. The proposed solutions either oversimplify the parameter model, or result in exponential complexity on D. In this paper, the exact expression for the soft metrics in the presence of parametric uncertainty modeled as a deterministic constant is rederived in a novel way. Based on this expression, suboptimal algorithms with linear complexity on D and N are presented. The applicability of the proposed algorithms is demonstrated with two examples, namely serially concatenated convolutional codes (SCCC) with carrier phase tracking, and trellis coded modulation (TCM) in frequency-selective fading channels